Characters and Blocks of Finite Groups / Gabriel Navarro.

By: Navarro, Gabriel [author.]Material type: TextTextSeries: London Mathematical Society Lecture Note Series ; no. 250Publisher: Cambridge : Cambridge University Press, 1998Description: 1 online resource (300 pages) : digital, PDF file(s)Content type: text Media type: computer Carrier type: online resourceISBN: 9780511526015 (ebook)Other title: Characters & Blocks of Finite GroupsSubject(s): Finite groups | Characters of groups | Blocks (Group theory)Additional physical formats: Print version: : No titleDDC classification: 512/.2 LOC classification: QA177 | .N38 1998Online resources: Click here to access online Summary: This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.
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This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.

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